Fabrice Barthélémy

Optimal holding period for a real estate portfolio

This paper considers the use of simulated cash flows to determine the optimal holding period of a real estate portfolio to maximize its present value. The traditional DCF approach with an estimation of the resale value through a growth rate of the future cash flow does not let appear this optimum. However, if the terminal value is calculated from the trend of a diffusion process of the price, an optimum may appear under certain conditions. Finally we consider the sensitivity of the present value to the different parameters involved in the cash flow estimations.

Using rents and price dynamics in real estate portfolio valuation

Purpose – The aim of this paper is to use rent and price dynamics in the future cash flows in order to improve real estate portfolio valuation.Design/methodology/approach – Monte Carlo simulation methods are employed for the measurement of complex cash generating assets such as real estate assets return distribution. Important simulation inputs, such as the physical real estate price volatility estimator, are provided by results on real estate indices for Paris, derived in an article by Baroni et al..Findings – Based on a residential real estate portfolio example, simulated cash flows: provide more robust valuations than traditional DCF valuations; permit the user to estimate the portfolios price distribution for any time horizon; and permit easy values‐at‐risk (VaR) computations.Originality/value – The terminal value estimation is a core issue in real estate valuation. To estimate it, the proposed method is not based on an anticipated growth rate of cash flows but on the estimation of the trend and the ...

A Comparison Between the Methods of Apportionment Using Power Indices: the Case of the us Presidential Elections

In this paper we compare five well-known methods of apportionment, advanced respectively by Adams, Dean, Hill, Webster and Jefferson. The criterion used for this comparison is the minimization of the distance between a power vector and a population vector. Power is measured with the well-known Banzhaf power index; the populations are those of the constituent states of the U.S.A. We first explain the conditions under which this comparison has plausibility. We then compare apportionment methods in terms of their capacity to move power in states closer to their populations. The election of the U.S. President by an electoral college is studied by examining 22 censuses since 1790. Our analysis is largely based on that used in the book by Balinski and Young [2001]. The empirical findings are linked to theoretical results.

A repeat sales index robust to small datasets

As suggested by D. Geltner, commercial properties indices have to be built using repeat sales instead of hedonic indices. The repeat sales method is a means of constructing real estate price indices based on a repeated observation of property transactions. These indices may be used as benchmarks for real estate portfolio managers. But the investors in general are also interested in introducing real estate performance in their portfolio to enhance the efficient frontier. Thus, expected return and volatility are the two key parameters. To create and to improve contracts on real estate indices, trend and volatility of these indices must be robust regarding to the periodicity of the index and the volume of transactions. This paper aims to test the robustness of the trend and volatility estimations for two indices: the classical Weighted Repeat Sales (Case & Shiller 1987) and a PCA factorial index (Baroni, Barthelemy and Mokrane 2007). The estimations are computed from a dataset of Paris commercial properties. The main findings are the trend and volatility estimates are biased for the WRS index and not for the PCA factorial index when the periodicity increases. Consequently, the level of the index at the end of the computing period is significantly different for various periodicities in the case of the WRS index. Globally, the PCA factorial seems to be more robust to the number of transactions. Firstly, we present the two methodologies and then the dataset. Finally we test the impact of the number of transactions per period on the trend and volatility estimates for each index and we give an interpretation of the results.

Unit roots tests and SARIMA models

Abstract Differencing at order 1 removes the stochastic trend, and differencing at seasonal order s removes the seasonal peaks. We propose a joint unit root test at order 1 and at order s, and tabulation for this test.

The Impact of Lease Structures on the Optimal Holding Period for a Commercial Real Estate Portfolio

Purpose The purpose of this paper is to exhibit the impacts of lease duration and lease break options on the optimal holding period for a real estate asset or portfolio Methodology / approach We use a Monte Carlo simulation framework to simulate a real estate assets cash-flows in which lease structures (rents indexation patterns overall lease duration and break options) are explicitly taken into account. We assume that a tenant exercises his/her option to break a lease if the rent paid as higher than the market rental value of similar properties. We also model vacancy duration stochastically using Poissons law. Finally capital values and market rental values are simulated using specific stochastic processes. and are also assumed to be correlated. We derive the optimal holding period for the asset as the value that maximises its discounted value. which is the sum of the discounted free cash flows and the discounted terminal Findings We demonstrate that. consistent with existing capital markets literature and real estate business practice. break-options in leases can dramatically alter optimal holding periods for real estate assets and portfolios by extension. We show that. everything else being equal. shorter lease durations. higher market rental value volatility. increasing negative rental reversion. higher vacancy duration. more break options. all tend to decrease the optimal holding period of a real estate asset. The converse is also true. Practical implications Practitioners are insights as well as a practical methodology for determining the ex-ame optimal holding period for an asset or a portfolio based on a number of market and asset specific parameters including the lease structure. Originality / value The originality of the paper derives from taking an explicit modelling approach to lease duration and lease breaks as additional sources of asset specific risk alongside market risk. This is critical in real estate portfolio management because such specific risk is usually difficult to diversify.

Ex-ante real estate Value at Risk calculation method

The computation of Value at Risk (VaR) has long been a problematic issue in commercial real estate. Difficulties mainly arise from the lack of appropriate data, the lack of transactions, the non-normality of returns, and the inapplicability of many of the traditional methodologies. In addition, specific risks remain latent in investors’ portfolios and thus risk measurements based on market index do not represent the risks of a specific portfolio. Following a spate of new regulations such as Basel II, Basel III, NAIC and Solvency II, financial institutions have increasingly been required to estimate and control their exposure to market risk. Hence, financial institutions now commonly use “internal” VaR (or Expected Shortfall) models in order to assess their market risk exposure. This paper proposes the first model designed especially for static real estate VaR computation. The proposal accounts for specific real estate characteristics such that the lease structures or the vacancies. The paper contributes to the real estate risk management literature by proposing for the first time a model that incorporates characteristics of real estate investments. It allows more precise real estate risk measurements and is derived from a regulators’ approach.

Market heterogeneity and the determinants of Paris apartment prices: A quantile regression approach

In this paper, the heterogeneity of the Paris apartment market is addressed. For this purpose, quantile regression is applied – with market segmentation based on price deciles – and the hedonic price of housing attributes is computed for various price segments of the market. The approach is applied to a major data set managed by the Paris region notary office (Chambre des Notaires d’Île de France), which consists of approximately 156,000 transactions over the 2000–2006 period. Although spatial econometric methods could not be applied owing to the unavailability of geocodes, spatial dependence effects are shown to be adequately accounted for through an array of 80 location dummy variables. The findings suggest that the relative hedonic prices of several housing attributes differ significantly among deciles. In particular, the elasticity coefficient of the apartment size variable, which is 1.09 for the cheapest units, is down to 1.03 for the most expensive ones. The unit floor level, the number of indoor parking slots, as well as several neighbourhood attributes and location dummies all exhibit substantial implicit price fluctuations among deciles. Finally, the lower the apartment price, the higher the potential for price appreciation over time. While enhancing our understanding of the complex market dynamics that underlie residential choices in a major metropolis such as Paris, this research provides empirical evidence that the QR approach adequately captures heterogeneity among house price ranges, which simultaneously applies to housing stock, historical construct and social fabric.

On the likelihood of dummy players in weighted majority games

When the number of players is small in a weighted majority voting game, it can occur that one of the players has no influence on the result of the vote, in spite of a strictly positive weight. Such a player is called a “dummy” player in game theory. The purpose of this paper is to investigate the conditions that give rise to such a phenomenon and to compute its likelihood. It is shown that the probability of having a dummy player is surprisingly high and some paradoxical results are observed.

Combining Monte Carlo Simulations and Options to Manage the Risk of Real Estate Portfolios

This paper aims to show that the accuracy of real estate portfolio valuations can be improved through the simultaneous use of Monte Carlo simulations and options theory. Our method considers the options embedded in Continental European lease contracts drawn up with tenants who may move before the end of the contract. We combine Monte Carlo simulations for both market prices and rental values with an optional model that takes into account a rational tenant’s behavior. We analyze to what extent the options exercised by the tenant significantly affect the owner’s income. Our main findings are that simulated cash flows which take account of such options are more reliable that those usually computed by the traditional method of discounted cash flow. Moreover, this approach provides interesting metrics, such as the distribution of cash flows. The originality of this research lies in the possibility of taking the structure of the lease into account. In practice this model could be used by professionals to improve the relevance of their valuations: the output as a distribution of outcomes should be of interest to investors. However, some limitations are inherent to our model: these include the assumption of the rationality of tenant’s decisions, and the difficulty of calibrating the model, given the lack of data. After a brief literature review of simulation methods used for real estate valuation, the paper describes the suggested simulation model, its main assumptions, and the incorporation of tenant’s decisions regarding break options influencing the cash flows. Finally, using an empirical example, we analyze the sensitivity of the model to various parameters, test its robustness and note some limitations.